Finding Constants for a Piecewise Defined Function

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In summary, the conversation is about finding constants a and b in a function and the use of typesetting formulas. The main focus is on ensuring continuity in the function.
  • #1
Mille89
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hi(Smile)
I need some start help finding the two constants a and b:

Do i start like this?:
\(\displaystyle \lim_{{x}\to{6-}} (20) = \lim_{{x}\to{6+}} (8x+a)\)View attachment 8782
 

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  • #2
Hi, and welcome to the forum.

Do i start like this?:
\lim_{{x}\to{6-}} (20) = \lim_{{x}\to{6+}} (8x+a)
If you need the function to be continuous, then yes.

You can typeset your formulas by enclosing them in [MATH]...[/MATH] tags (button with $\sum$ on the toolbar) or dollar signs.
 
  • #3
Evgeny.Makarov said:
Hi, and welcome to the forum.

If you need the function to be continuous, then yes.

You can typeset your formulas by enclosing them in [MATH]...[/MATH] tags (button with $\sum$ on the toolbar) or dollar signs.

Thank you(Smile)(Yes)
 

FAQ: Finding Constants for a Piecewise Defined Function

What is a piecewise defined function?

A piecewise defined function is a mathematical function that is defined by different formulas or expressions on different intervals or domains. This allows for different rules to be applied to different parts of the function.

How is a piecewise defined function written?

A piecewise defined function is typically written using a combination of the "if" and "else" statements. For example:
f(x) = {
     x + 1, if x < 0
     x^2, if x ≥ 0
}

What is the purpose of using a piecewise defined function?

The purpose of using a piecewise defined function is to have different rules or behaviors for different parts of the function. This allows for more complex and accurate representations of real-world situations.

Can a piecewise defined function have more than two pieces?

Yes, a piecewise defined function can have multiple pieces, each with its own rule or expression. The number of pieces is not limited, but it is important to ensure that the pieces are well-defined and do not overlap.

How do you graph a piecewise defined function?

To graph a piecewise defined function, you can graph each piece separately and then combine them on the same graph. It is important to pay attention to the domain and range of each piece to ensure the graph accurately represents the function.

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